Non-thin rational points for elliptic K3 surfaces
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929308784656384 |
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| author | Gvirtz-Chen, Damián Mezzedimi, Giacomo |
| author_facet | Gvirtz-Chen, Damián Mezzedimi, Giacomo |
| contents | We prove that elliptic K3 surfaces over a number field which admit a second elliptic fibration satisfy the potential Hilbert property. Equivalently, the set of their rational points is not thin after a finite extension of the base field. Furthermore, we classify those families of elliptic K3 surfaces over an algebraically closed field which do not admit a second elliptic fibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-thin rational points for elliptic K3 surfaces Gvirtz-Chen, Damián Mezzedimi, Giacomo Algebraic Geometry Number Theory 14J28, 14G05 (Primary) 14J27, 11R45, 06B05 (Secondary) We prove that elliptic K3 surfaces over a number field which admit a second elliptic fibration satisfy the potential Hilbert property. Equivalently, the set of their rational points is not thin after a finite extension of the base field. Furthermore, we classify those families of elliptic K3 surfaces over an algebraically closed field which do not admit a second elliptic fibration. |
| title | Non-thin rational points for elliptic K3 surfaces |
| topic | Algebraic Geometry Number Theory 14J28, 14G05 (Primary) 14J27, 11R45, 06B05 (Secondary) |
| url | https://arxiv.org/abs/2404.06844 |